The authorities require the certification that aircraft meet certain requirements so that they can fly, which requirements ensure their operability in meteorological conditions favoring continuous or intermittent ice formation.
There are many types of problems caused by ice in airplanes. During the landing, the airplane can descend with an intermediate speed from a cold and dry flight altitude to a normal situation on the ground passing through cloudy areas in which moisture or water particles can freeze on the airplane surfaces that are still cold. This can cause a weight increase and a change in the aerodynamic shape especially in the leading edges of wings, tail stabilizers and engine air intake ducts. At an altitude of 17,000 feet and 10,000 feet, the types of ice causing risks are different. In airfoils with ice, the aerodynamic behavior changes dramatically in a low-speed landing configuration: the lift is reduced, the drag increases and they can unexpectedly stall. Due to the ice in the horizontal and vertical stabilizers, the airplane can lose side or longitudinal control. The largest ice particles, which break upon coming into contact with the engine air intake ducts, can damage the blades or sensors of the turbofans.
Due to the above, critical airplane surfaces must be protected from ice by means of suitable systems. These systems increase the airplane weight and must therefore desirably be as efficient as possible.
To deal with the aforementioned problems, the development of analytical models which allow evaluating both the accumulated ice and the effect caused by it on the airplane is considered to be essential. These analytical models also allow a more efficient evaluation of the protection systems against ice during the airplane design stage.
The known analytical models which allow calculating ice formations generally include at least the following modules:                A fluid field calculation module for calculating the fluid field around the surface in question.        A water uptake calculation module.        An ice growth and thermodynamic balance calculation module.        
The water uptake module comprises a simulator which must accurately represent the water accumulation process occurring when an aircraft traverses a cloud containing water droplets that are cold enough to become frozen, for the purpose of being able to calculate the uptake parameter of the surface, which parameter will be used in the ice growth and thermodynamic balance calculation module.
The way to obtain the uptake parameter, using Lagrange modeling, consists of carrying out a massive droplet projection, resolving the paths of such droplets and studying the impacts occurring on the outer aircraft surface. In this situation, it is important to establish the initial water droplet distribution in the cloud and the physical properties of such droplets because their paths will depend on such properties, which paths are required to determine the uptake amount (total uptake efficiency), distribution (local uptake efficiency) and extension (limits of the impacted surface).
In the known art, the way to obtain the local uptake efficiency parameter for three-dimensional cases consists of calculating the area ratio between the triangles formed by three water droplets coming out of the projection area and the triangle formed by their impacts on the study surface.
Thus, in reference to FIG. 2, the local uptake efficiency parameter is given by the expression
      β    =                  A        ⁢                                  ⁢        2                    A        ⁢                                  ⁢        1              ,where A1 is the area of the triangle that would be formed by three close particles on the projection plane, and A2 is the area of the triangle that would be formed by their impact points on the aerodynamic surface.
This parameter is calculated for each of the different particle sizes and the contribution of each particle is added according to the formula:
            β      ⁡              (        s        )              =                  ∑                  i          =          1                N            ⁢                          ⁢                        n          i                ⁢                              β            i                    ⁡                      (            s            )                                ,where ni is the liquid mass fraction associated to the size of particle i and N is the number of particle sizes used to characterize the distribution. βi is the local uptake efficiency parameter calculated for particle i.
This process requires carrying out as many uptake calculations as different particle sizes considered in the distribution, as it is not possible to use different particle sizes in the same calculation because the local uptake parameter calculation is based on the hypothesis that all the particles that come out within triangle A1 impact on the triangle defined by A2 (mass continuity condition), which hypothesis is only valid if it is considered that all the particles have the same size.
The method known in the art therefore has a high computation cost, especially when working with very complex geometries. The present invention is aimed at solving this drawback both in the calculation of water droplet uptake by aircraft surfaces and in the calculation of the uptake of another type of particles by another type of surfaces moving in a flow current.